Chapter 22 - Induction and Alternating Current Important Equations to Know
Terms and Laws
electromagnetic induction
emf
Lenz's Law
Faraday's Law
generator
rms vs. maximum (current, potential difference)
alternating and direct current
motors
back emf
mutual inductance
transformersMain Points
Changing the magnetic field strength near a conductor induces an emf.
The direction of an induced current in a circuit is such that its magnetic field opposes the change in the applied magnetic field.
Generators use induction to convert mechanical energy into electrical energy.
Alternating current is measured in terms of rms current.
Motors use an arrangement similar to that of generators to convert electrical energy into mechanical energy.
Mutual inductance involves the induction of a current in one circuit by means of changing current in a nearby circuit.
Transformers change the potential difference of an alternating current.
Electromagnetic Induction You don't need wires or a power supply to create a current. Instead, you can move a wire in a magnetic field to produce a current. This process is referred to as electromagnetic induction. Electromagnetic induction is defined as producing an emf in a circuit by changing the magnetic field. To change the field, you can change the position, strength, or orientation of the external magnetic field. To review, emf is rate of change of magnetic flux on the loop. This is very similar to potential difference. Basically, electromagnetic induction works like this:
1. Magnetic fields make moving charges deflect.
2. Charges moving with a velocity at an angle to a magnetic field experience a force (right hand rule).
3. This force is a lot like potential difference, because it makes the charges move.
4. Remember, the wire must be moving and it must cross magnetic field lines.
Lenz's Law Emf is greatest when the plane of the loop is perpendicular to magnetic field lines. It decreases and becomes zero as the loop rotates to become parallel to the field lines. Also, an increase in the number of field lines (which is increasing the field strength) or increase in the area of the loop will increase the induced current.
The current induced will be opposed by the magnetic field it approaches. As the current's magnetic field get stronger, so does the opposition to it, which leads to Lenz's law: The magnetic field of the induced current opposes the change in the applied magnetic field.When the magnet moves away, the field lessens, as does the opposition to it. We can use this law to find the direction of an induced current. To find the emf, we use Faraday's Law of Induction.
Faraday's Law
N is the number of turns in a coil; a negative sign preceds it to indicate the polarity of the induced emf (Lenz's law). A is the area of the coil. B is the field strength. Theta is the angle of orientation, or the angle between the normal of the loop and the field lines. Delta t is the change in time. PRACTICE 3. A circular wire loop with a radius of 0.33 m is located in an external magnetic field of strength 0.25 T that is perpendicular to the plane of the loop.The field strength changes to -0.35 T in 1.5s.Find the magnitude of the average induced emf during the interval (Faughn 800).
Applications of Induction
Induction has a variety of applications, including doorbells and tape recorders. In a doorbell, when the button is pressed, the light bulb behind the button goes out, signaling a break in the circuit. This circuit break is used to induce a series current on coils of wire, which force an iron plunger in a chime. In a tape recorder, sound waves are converted into electric current. The tape recorder has an iron ring with a gap with wires wrapped around it. As the current passes through the wire, the changes in the magnetic field are recorded on the magnetic tape of the recorder. They can then be played back and converted into sound waves.
Generator Another application of induction is the generator. Moving a wire throughout a magnetic field induces a current. Twirling the wire will have the same effect as moving the wire in and out of the field. Moving the wire is an example of mechanical motion. Instead of having a person generate this motion, one can connect the wire to a device that will generate the motion.
When the loop of wire is perpendicular to the magnetic field, it is parallel to the field and does not cross field lines. This means an emf will not be generated. However, when the loop is parallel to the field, its wires will cross the magnetic field lines, and an emf will be generated.
(Faughn 804).
As the loop rotates, the emf it creates changes direction. The emf moves from zero to positive to zero to negative. In part a, the two main sections of the wire are parallel to the field lines, so no emf is induced. B and d are outside of the field, so no emf can be induced upon them. As the wire continuously moves, the emf is continuously changing.
Alternating Current Because the emf changes constantly, it produces a constantly changing current. This current is called alternating current because it changes direction every 1/60th of a second. This change is not noticeable, because it happens too fast for the human eye to perceive. Note: Resistors work in both alternating and direct current because they resist the flow of current, regardless of its direction.
Rms and Max (Current and Potential Difference)
Current and potential difference fluctuate from a maximum to zero to a minimum. To get a consistent measurement, we use an average called rms, or root mean square. Rms current is the amount of direct current that would dissipate the same amount of energy as alternating current in a resistor at the same cycle. Current is measured in rms values, so the maximum value is actually larger than the rms value. The relationship between rms current and maximum current is:
Rms potential difference has similar relationship to maximum potential difference as rms current has to maximum current.
In the US, potential difference is measured in rms values at 120 Volts. The maximum value possible, however is about 170 Volts. Note: Ohm's law holds for rms values.
PRACTICE 1. What is the rms current in a light bulb that has a resistance of 25 Ω and a rms potential difference of 120 V ? What are the maximum values for current and potential difference? (Faughn 810).
Motors Motors work in the opposite direction of generators, they convert electrical energy into mechanical energy. It is the same set-up as an alternating current generator. As the coil in the motor rotates, it induces a back emf that acts like friction and reduces the current powering the motor. Mutual Inductance Two coils are wrapped around an iron ring. When the magnetic field in the primary changes, it induces an emf in the secondary. This is mutual inductance, or that ability of one current carrying circuit to influence an emf in a nearby circuit. The relationship between emf, M (constant for mutual inductance based on the system), current, and time using the following equation.
Transformers
Transformers use the principle of mutual inductance to convert potential differences of alternating currents to different strengths. They consist of a primary and secondary with N turns and V potential difference respectively.
If the secondary has more turns than the primary, it is a step-up transformer because it increases the potential difference. If the primary has more turns, the transformer is a step-down transformer because it reduces the potential difference. Transformers DO NOT violate the conservation of energy laws because the input power and output power are ideally the same.
In the real world, however, some power is lost due to small currents induced by changing magnetic fields in the iron core of the transformer, and due to resistance. Input power will always then be equal or greater than output power.
PRACTICE 5. A television picture tube requires a high potential difference, which in older models is provided by a step-up transformer. The transformer has 12 turns in its primary and 2550 turns in its secondary. If 120 V is placed across the primary, what is the output potential difference? (Faughn 818).
INDEPENDENT PRACTICE
1. An AC generator has a maximum output emf of 7.25 * 103V. What is the rms potential difference for this generator?
(5.13 * 103V)
2. A step up transformer used on a 240 V line has 27 turns on the primary and 8542 turns on the secondary. What is the potential difference across the secondary?
(7.6 * 104 V)
3. A loop of wire with 25 turns and an area of 0.0243 square meters is perpendicular to a magnetic field of strength 2.85 T. If the loop is removed from the field in a time interval of 1.20 seconds, what is the average emf in the wire?
(-1.44 V)
Self Induction, effective current, and maximum emf for a generator were not covered in class or tested.
CITATIONS
Faughn, Jerry S. and Raymond A. Serway. Physics. New York: Holt, 2004.
Strong, Tom. Course notes. Honors Physics, Dept. of Science, Mount Lebanon High School. May and June 2009.
Important Equations to Know
Terms and Laws
electromagnetic induction
emf
Lenz's Law
Faraday's Law
generator
rms vs. maximum (current, potential difference)
alternating and direct current
motors
back emf
mutual inductance
transformersMain Points
Electromagnetic Induction
You don't need wires or a power supply to create a current. Instead, you can move a wire in a magnetic field to produce a current. This process is referred to as electromagnetic induction. Electromagnetic induction is defined as producing an emf in a circuit by changing the magnetic field. To change the field, you can change the position, strength, or orientation of the external magnetic field. To review, emf is rate of change of magnetic flux on the loop. This is very similar to potential difference. Basically, electromagnetic induction works like this:
1. Magnetic fields make moving charges deflect.
2. Charges moving with a velocity at an angle to a magnetic field experience a force (right hand rule).
3. This force is a lot like potential difference, because it makes the charges move.
4. Remember, the wire must be moving and it must cross magnetic field lines.
Lenz's Law
Emf is greatest when the plane of the loop is perpendicular to magnetic field lines. It decreases and becomes zero as the loop rotates to become parallel to the field lines. Also, an increase in the number of field lines (which is increasing the field strength) or increase in the area of the loop will increase the induced current.
The current induced will be opposed by the magnetic field it approaches. As the current's magnetic field get stronger, so does the opposition to it, which leads to Lenz's law:
The magnetic field of the induced current opposes the change in the applied magnetic field.When the magnet moves away, the field lessens, as does the opposition to it. We can use this law to find the direction of an induced current. To find the emf, we use Faraday's Law of Induction.
Faraday's Law
N is the number of turns in a coil; a negative sign preceds it to indicate the polarity of the induced emf (Lenz's law). A is the area of the coil. B is the field strength. Theta is the angle of orientation, or the angle between the normal of the loop and the field lines. Delta t is the change in time.
PRACTICE
3. A circular wire loop with a radius of 0.33 m is located in an external magnetic field of strength 0.25 T that is perpendicular to the plane of the loop. The field strength changes to -0.35 T in 1.5s. Find the magnitude of the average induced emf during the interval (Faughn 800).
Applications of Induction
Induction has a variety of applications, including doorbells and tape recorders. In a doorbell, when the button is pressed, the light bulb behind the button goes out, signaling a break in the circuit. This circuit break is used to induce a series current on coils of wire, which force an iron plunger in a chime. In a tape recorder, sound waves are converted into electric current. The tape recorder has an iron ring with a gap with wires wrapped around it. As the current passes through the wire, the changes in the magnetic field are recorded on the magnetic tape of the recorder. They can then be played back and converted into sound waves.
Generator
Another application of induction is the generator. Moving a wire throughout a magnetic field induces a current. Twirling the wire will have the same effect as moving the wire in and out of the field. Moving the wire is an example of mechanical motion. Instead of having a person generate this motion, one can connect the wire to a device that will generate the motion.
When the loop of wire is perpendicular to the magnetic field, it is parallel to the field and does not cross field lines. This means an emf will not be generated. However, when the loop is parallel to the field, its wires will cross the magnetic field lines, and an emf will be generated.
(Faughn 804).
As the loop rotates, the emf it creates changes direction. The emf moves from zero to positive to zero to negative. In part a, the two main sections of the wire are parallel to the field lines, so no emf is induced. B and d are outside of the field, so no emf can be induced upon them. As the wire continuously moves, the emf is continuously changing.
Alternating Current
Because the emf changes constantly, it produces a constantly changing current. This current is called alternating current because it changes direction every 1/60th of a second. This change is not noticeable, because it happens too fast for the human eye to perceive. Note: Resistors work in both alternating and direct current because they resist the flow of current, regardless of its direction.
Rms and Max (Current and Potential Difference)
Current and potential difference fluctuate from a maximum to zero to a minimum. To get a consistent measurement, we use an average called rms, or root mean square. Rms current is the amount of direct current that would dissipate the same amount of energy as alternating current in a resistor at the same cycle. Current is measured in rms values, so the maximum value is actually larger than the rms value. The relationship between rms current and maximum current is:
Rms potential difference has similar relationship to maximum potential difference as rms current has to maximum current.
In the US, potential difference is measured in rms values at 120 Volts. The maximum value possible, however is about 170 Volts. Note: Ohm's law holds for rms values.
PRACTICE
1. What is the rms current in a light bulb that has a resistance of 25 Ω and a rms potential difference of 120 V ? What are the maximum values for current and potential difference? (Faughn 810).
Motors
Motors work in the opposite direction of generators, they convert electrical energy into mechanical energy. It is the same set-up as an alternating current generator. As the coil in the motor rotates, it induces a back emf that acts like friction and reduces the current powering the motor.
Mutual Inductance
Two coils are wrapped around an iron ring. When the magnetic field in the primary changes, it induces an emf in the secondary. This is mutual inductance, or that ability of one current carrying circuit to influence an emf in a nearby circuit. The relationship between emf, M (constant for mutual inductance based on the system), current, and time using the following equation.
Transformers
Transformers use the principle of mutual inductance to convert potential differences of alternating currents to different strengths. They consist of a primary and secondary with N turns and V potential difference respectively.
If the secondary has more turns than the primary, it is a step-up transformer because it increases the potential difference. If the primary has more turns, the transformer is a step-down transformer because it reduces the potential difference. Transformers DO NOT violate the conservation of energy laws because the input power and output power are ideally the same.
In the real world, however, some power is lost due to small currents induced by changing magnetic fields in the iron core of the transformer, and due to resistance. Input power will always then be equal or greater than output power.
PRACTICE
5. A television picture tube requires a high potential difference, which in older models is provided by a step-up transformer. The transformer has 12 turns in its primary and 2550 turns in its secondary. If 120 V is placed across the primary, what is the output potential difference? (Faughn 818).
INDEPENDENT PRACTICE
1. An AC generator has a maximum output emf of 7.25 * 103 V. What is the rms potential difference for this generator?
(5.13 * 103 V)
2. A step up transformer used on a 240 V line has 27 turns on the primary and 8542 turns on the secondary. What is the potential difference across the secondary?
(7.6 * 104 V)
3. A loop of wire with 25 turns and an area of 0.0243 square meters is perpendicular to a magnetic field of strength 2.85 T. If the loop is removed from the field in a time interval of 1.20 seconds, what is the average emf in the wire?
(-1.44 V)
Self Induction, effective current, and maximum emf for a generator were not covered in class or tested.
CITATIONS
Faughn, Jerry S. and Raymond A. Serway. Physics. New York: Holt, 2004.
Strong, Tom. Course notes. Honors Physics, Dept. of Science, Mount Lebanon High School. May and June 2009.